Input-output finite-time stability and stabilization of stochastic Markovian jump systems

In this paper, we introduce a new concept named input-output finite-time mean square stability (IO-FTMSS) for stochastic Markovian jump systems. In contrast to the available notions of stochastic stability, IO-FTMSS characterizes the input-output behavior of dynamics on a finite time horizon. Concerning a class of random input signals L_T², the problems of input-output finite-time mean square stability and stabilization are investigated for both linear and nonlinear stochastic systems perturbed by Markovian processes. Sufficient conditions are derived in terms of coupled linear matrix inequalities (LMIs) and Hamilton-Jacobi inequalities (HJIs), respectively. In addition, a numerical example is supplied to illustrate the proposed technique.